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Questions and Answers of College Algebra

Solve each equation, and check the solution. 5 9 x = 2
Solve each equation, and check the solution. 3 11 -X = -5
A certificate of deposit for 1 yr pays $25.50 simple interest on a principal of $3400. What is the interest rate being paid on this deposit?
A real-estate agent earned $6300 commission on a property sale of $210,000. What is her rate of commission?
Suppose that in solving the following equation, we multiply each side y 12, rather than the least common denominator, 6. Would we obtain the correct solution? Explain. 1 -x+ 3 1 2 || 1 -x 6
A mixture of acid and water is 35% acid. If the mixture contains a total of 40 L, how many liters of pure acid are in the mixture? How many liters of pure water are in the mixture?
To solve the following linear equation, we multiply each side by the least common denominator of all the fractions in the equation. What is this LCD? 3 -X 4 1 5 =x=-x-5 6 3
Copy paper also comes in legal size, which has the same width but is longer than standard size. If a ream of legal-size paper has the same thickness as standard-size paper and a volume of 238 in.3,
A mixture of alcohol and water contains a total of 36 oz of liquid. There are 9 oz of pure alcohol in the mixture. What percent of the mixture is water? What percent is alcohol?
In a flock of 30 geese, 15 are male. What percent are not male?
The expression 0.06(10 - x)(100) is equivalent to which one of the following?A. 0.06 - 0.06x B. 60 - 6x C. 6 - 6x D. 6 - 0.06x
In a group of 12 children, 3 are girls. What percent are not girls?
To solve a linear equation with decimals, we usually begin by multiplying by a power of 10 so that all coefficients are integers. What is the least power of 10 that will accomplish this goal in each
A closet containing 50 shoes has 12 that are black. What percent of the shoes are black?
A jar of 20 coins contains 4 pennies. What percent of the coins are pennies?
A sheet of standard-size copy paper measures 8.5 in. by 11 in. If a ream (500 sheets) of this paper has a volume of 187 in.3, how thick is the ream? Office Plus Copy paper -8.5 in. - 11 in.
Marina City in Chicago is a complex of two residential towers that resemble corncobs. Each tower has a concrete cylindrical core with a 35-ft diameter and is 588-ft tall. Find the volume of the core
15 is what percent of 150?
The radius of a circle is 2.5 in.(a) What is its diameter?(b) What is its circumference? r = 2.5 in.
Solve each equation, and check the solution. If applicable, tell whether the equation is an identity or a contradiction.4[6 - (1 + 2x) ] + 10x = 2(10 - 3x) + 8x
The circumference of a circle is 480π in.(a) What is its radius?(b) What is its diameter? d r
12 is what percent of 48?
Solve each equation, and check the solution. If applicable, tell whether the equation is an identity or a contradiction.7[2 - (3 + 4x)] - 2x = -9 + 2(1 - 15x)
Solve each equation, and check the solution. If applicable, tell whether the equation is an identity or a contradiction.4(x + 2) - 8x - 5 = -3x + 9 - 2(x + 6)
The base of the Great Pyramid of Cheops is a square whose perimeter is 920 m. What is the length of each side of this square? Pump Perimeter = 920 m
Solve each equation, and check the solution. If applicable, tell whether the equation is an identity or a contradiction.-3x + 6 - 5(x - 1) = -5x - (2x - 4) + 5
Solve each equation, and check the solution. If applicable, tell whether the equation is an identity or a contradiction.- [6x - (4x + 8)] = 9 + (6x + 3)
Solve each equation, and check the solution. If applicable, tell whether the equation is an identity or a contradiction.- [2x - (5x + 2)] = 2 + (2x + 7)
Solve each equation, and check the solution. If applicable, tell whether the equation is an identity or a contradiction.4[2x - (3 - x) + 5] = -(2 + 7x)
Solve each equation, and check the solution. If applicable, tell whether the equation is an identity or a contradiction.2[x - (2x + 4) + 3] = 2(x + 1)
Solve each equation, and check the solution. If applicable, tell whether the equation is an identity or a contradiction.4(2x + 7) = 2x + 25 + 3(2x + 1)
Solve each equation, and check the solution. X 5 X | 4 = 1
As of 2017, the highest temperature ever recorded in the state of Washington was 42°C. Find the corresponding Fahrenheit temperature to the nearest degree.
Solve each equation for y. 1 -X 2 1 3* = 1 =
Solve each equation, and check the solution. If applicable, tell whether the equation is an identity or a contradiction.-2(x + 3) - x - 4 = -3(x + 4) + 2
The distance from Melbourne to London is 10,500 mi. If a jet averages 500 mph between the two cities, what is its travel time in hours?
Solve each equation, and check the solution. If applicable, tell whether the equation is an identity or a contradiction.-2x - 3(4 - 2x) = 2(x - 3) + 2
Nora traveled from Kansas City to Louisville, a distance of 520 mi, in 10 hr. Find her rate in miles per hour.
Solve each equation, and check the solution. If applicable, tell whether the equation is an identity or a contradiction.6x - 4(3 - 2x) = 5(x - 4) - 10
In 2007, rain shortened the Indianapolis 500 race to 415 mi. It was won by Dario Franchitti, who averaged 151.774 mph. What was his time to the nearest thousandth?
Solve each equation, and check the solution. If applicable, tell whether the equation is an identity or a contradiction.6x - 3(5x + 2) = 4(1 - x)
Kurt Busch won the Daytona 500 (mile) race with a rate of 143.187 mph in 2017. Find his time to the nearest thousandth.
Solve each equation, and check the solution. If applicable, tell whether the equation is an identity or a contradiction.2x + 3(x - 4) = 2(x - 3)
Solve each equation, and check the solution. If applicable, tell whether the equation is an identity or a contradiction.4(x - 2) + 2(x + 3) = 6
Solve each equation, and check the solution. If applicable, tell whether the equation is an identity or a contradiction.3(2x + 1) - 2(x - 2) = 5
Solve each equation for y.8x - 3y = 4
Solve each equation, and check the solution. If applicable, tell whether the equation is an identity or a contradiction.-4(x - 9) = -8(x + 3)
Solve each equation for y.6x - 5y = 7
Solve each equation, and check the solution. If applicable, tell whether the equation is an identity or a contradiction.-2(x + 3) = -6(x + 7)
The formulacan be solved for C to obtainWhich one of the following is not equivalent to this? 9 F = ²C + 32
Solve each equation for y.-5x + 3y = 12
Solve each equation, and check the solution. If applicable, tell whether the equation is an identity or a contradiction.-6x + 2x - 11 = -2(2x - 3) + 4
When a formula is solved for a particular variable, several different equivalent forms may be possible. If we solvefor h, one correct answer isWhich one of the following is not equivalent to this?
Solve each equation for y.-3x + 2y = 5
Solve each equation, and check the solution. If applicable, tell whether the equation is an identity or a contradiction.-2x + 5x - 9 = 3(x - 4) - 5
Solve each equation for y.7x + 8y = 11
Solve each equation, and check the solution. If applicable, tell whether the equation is an identity or a contradiction.5(x + 3) + 4x - 5 = 4 - 2x
Solve each equation for y.4x + 9y = 11
Solve each equation, and check the solution. If applicable, tell whether the equation is an identity or a contradiction.-5(x + 1) + 3x + 2 = 6x + 4
Solve each equation for y.x - 5y = -20
Solve each equation, and check the solution. If applicable, tell whether the equation is an identity or a contradiction.2(3 - 2x) = x - 4
Solve each equation, and check the solution. If applicable, tell whether the equation is an identity or a contradiction.3(2t - 4) = 20 - 2t
Solve each equation for y.x - 2y = -6
Solve each equation, and check the solution. If applicable, tell whether the equation is an identity or a contradiction.-4x + 5x - 8 + 4 = 6x - 4
Solve each formula for the specified variable. 5/9 C=(F32) for F (Fahrenheit to Celsius)
Solve each equation for y.3x + y = 9
Solve each equation, and check the solution. If applicable, tell whether the equation is an identity or a contradiction.12w + 15w - 9 + 5 = -3w + 5 - 9
Solve each equation, and check the solution. If applicable, tell whether the equation is an identity or a contradiction.2x + 4 - x = 4x - 5
Which one of the following linear equations does not have solution set {all real numbers}? A. 4x = 5xx C. 4x = 3x E. 4(x - 2) = 2(2x - 4) B. 3(x + 4) = 3x + 12 3 D. ²/x = D. x = 0.75x 4 F. 2x18x =
This incorrect solution contains a common error.Give the correct solution. 12 2(3x + 1) = 11 10(3x + 1) = 11 30x10 11 30x = 1 1 30 X =
Solve each formula for the specified variable. V=r²h for h (volume of a cone)
Solve each equation, and check the solution. If applicable, tell whether the equation is an identity or a contradiction.7x - 5x + 15 = x + 8
Suppose we solve a linear equation and obtain, as our final result, an equation in Column I. Match each result with the solution set in Column II for the original equation. I (a) 7 = 7 (b) x = 0 (c)
This incorrect solution contains a common error.Give the correct solution. 8x2(2x-3) 8x4x6 = 3x + 7 = 3x + 7 4x6 = 3x + 7 x = 13
Solve each formula for the specified variable. 9 F=C+32 for C 5 (Celsius to Fahrenheit)
Solve each equation, and check the solution. If applicable, tell whether the equation is an identity or a contradiction.9x + 1 = 7x - 9
Solve each formula for the specified variable.M = C(1 + r) for r(markup)
Solve each formula for the specified variable. V = Tr²h for h (volume of a right circular cylinder) h
Solve each equation, and check the solution. If applicable, tell whether the equation is an identity or a contradiction.5x + 2 = 3x - 6
Solve each formula for the specified variable. A = 1/2 h (b + h(b + B) (area of a trapezoid) (b) for B (a) for b b B-
Solve each formula for the specified variable.A = P(1 + rt) for t(future value for simple interest)
Solve each equation, and check the solution. If applicable, tell whether the equation is an identity or a contradiction.5x - 4 = 21
Solve each formula for the specified variable.y = mx + b(slope-intercept form of a linear equation)(a) For x (b) For m
Solve each equation, and check the solution. If applicable, tell whether the equation is an identity or a contradiction.7x + 8 = 1
Solve each formula for the specified variable. 1==12bh bh (area of a triangle) (a) for h (b) for b ·b-
Solve each formula for the specified variable.ax + b = 0(linear equation in x)(a) For x (b) For a
Solve each formula for the specified variable. C = 2πr for r (circumference of a circle) r
Solve each formula for the specified variable. V = LWH (volume of a rectangular solid) (a) for W (b) for H H W L
Solve each formula for the specified variable. P= a + b + c (perimeter of a triangle) (a) for b (b) for c a C b
Solve each formula for the specified variable. P = 2L + 2W for L (perimeter of a rectangle) L W
Determine whether each of the following is an expression or an equation.-10x + 12 - 4x + 3 = 0
Solve each formula for the specified variable. A = bh (area of a (a) for b -b parallelogram) (b) for h
Determine whether each of the following is an expression or an equation.-10x + 12 - 4x = -3
Determine whether each of the following is an expression or an equation.4(x + 3) - 2(x + 1) + 10
Solve each formula for the specified variable. A = LW (area of a rectangle) (a) for W (b) for L L W
Complete each statement. The following key terms may be used once, more than once, or not at all.A linear equation with no solution is a(n) _________ . Its solution set is the _________ . linear
Determine whether each of the following is an expression or an equation.4(x + 3) - 2(x + 1) - 10
Complete each statement. The following key terms may be used once, more than once, or not at all.A linear equation with an infinite number of solutions is a(n) _________ . Its solution set is
Determine whether each of the following is an expression or an equation.-3x + 2 - 4 - x = 4
Determine whether each of the following is an expression or an equation.-3x + 2 - 4 = x

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